Please Show Each and Every Working VERY CLEARLY. There are NO multi-questions here, only just multi-PART questions which are CONNECTED to each other, and hence, Please do NOT Leave any, Thank You!Please Answer (i) Q2 Consider the Cobb-Douglas utility function, u;(X, Y) = Xª Y' -ª for a rational consumeri. Derive the Marshallian demand functions for X and Y.ii. Use the Marshallian demand functions for X and Y above to compute the indirectutility function and the expenditure function.iii. Using the expenditure function obtained in part (ii) together with Shephard's lemma,derive the Hicksian compensated demand function for X and Y.iv. Suppose a = 0.5, Px = Py = $2, M (money income per week) = $100, find theconsumer's optimal bundle. Illustrate your results graphically as well.v. If the government gives $10 financial support weekly for each family during theCOVID-19 lockdown period, how would the results be changed in iv? Whilepresenting the calculations clearly, illustrate the outcome graphically.

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Economics

Marshallian demand functions fa

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.13P

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Please Show Each and Every Working VERY CLEARLY. There are NO multi-questions here, only just multi-PART questions which are CONNECTED to each other, and hence, Please do NOT Leave any, Thank You! Please Answer (i)

Q2 Consider the Cobb-Douglas utility function, u;(X, Y) = Xª Y' -ª for a rational consumer
i. Derive the Marshallian demand functions for X and Y.
ii. Use the Marshallian demand functions for X and Y above to compute the indirect
utility function and the expenditure function.
iii. Using the expenditure function obtained in part (ii) together with Shephard's lemma,
derive the Hicksian compensated demand function for X and Y.
iv. Suppose a = 0.5, Px = Py = $2, M (money income per week) = $100, find the
consumer's optimal bundle. Illustrate your results graphically as well.
v. If the government gives $10 financial support weekly for each family during the
COVID-19 lockdown period, how would the results be changed in iv? While
presenting the calculations clearly, illustrate the outcome graphically.

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